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n + [n*r/s] + [n*t/s]; r=1, s=sin(2*Pi/5), t=csc(2*Pi/5).
5

%I #15 Sep 08 2022 08:45:56

%S 3,6,9,12,15,18,21,24,27,31,34,37,40,43,46,49,52,55,59,63,66,69,72,75,

%T 78,81,84,87,91,94,97,100,103,106,109,112,115,119,123,126,129,132,135,

%U 138,141,144,147,151,154,157,160,163,166,169,172,175,179,182,186,189,192,195,198,201,204,207,211,214,217,220,223,226,229,232,235

%N n + [n*r/s] + [n*t/s]; r=1, s=sin(2*Pi/5), t=csc(2*Pi/5).

%C See A190082.

%H G. C. Greubel, <a href="/A190083/b190083.txt">Table of n, a(n) for n = 1..10000</a>

%F (See A190082.)

%t r=1; s=Sin[2*Pi/5]; t=Csc[2*Pi/5];

%t a[n_] := n + Floor[n*s/r] + Floor[n*t/r];

%t b[n_] := n + Floor[n*r/s] + Floor[n*t/s];

%t c[n_] := n + Floor[n*r/t] + Floor[n*s/t];

%t Table[a[n], {n, 1, 120}] (* A190082 *)

%t Table[b[n], {n, 1, 120}] (* A190083 *)

%t Table[c[n], {n, 1, 120}] (* A190084 *)

%o (PARI) for(n=1,100, print1(n + floor(n/sin(2*Pi/5)) + floor(n/(sin(2*Pi/5))^2), ", ")) \\ _G. C. Greubel_, Nov 07 2018

%o (Magma) R:= RealField(); [n + Floor(n/Sin(2*Pi(R)/5)) + Floor(n/(Sin(2*Pi(R)/5))^2): n in [1..100]]; // _G. C. Greubel_, Nov 07 2018

%Y Cf. A190082, A190084.

%K nonn

%O 1,1

%A _Clark Kimberling_, May 04 2011